Intermediate Algebra for College Students (7th Edition)

by
Blitzer, Robert F.

Published by
Pearson

ISBN 10:
0-13417-894-7

ISBN 13:
978-0-13417-894-3

Chapter 1 - Test - Page 101: 11

Answer

$\dfrac{1}{4}$

Work Step by Step

RECALL:
$a-b = a+(-b)$
Use the rule above to obtain:
$=-\frac{1}{4} + -(-\frac{1}{2})
\\=-\frac{1}{4} + \frac{1}{2}$
Make the fractions similar using their LCD of $4$ to obtain:
$=-\frac{1}{4} + \frac{2}{4}$
The addends have opposite signs so subtract their absolute values to obtain:
$|\frac{2}{4}| - |-\frac{1}{4}| = \frac{2}{4}-\frac{1}{4} = \frac{1}{4}$
The sum will have the same sign as the number with the bigger absolute value.
The positive number has a bigger absolute value so the sum of the two numbers must be positive.
Thus, the answer is $\dfrac{1}{4}$.